What Is The Odds Of Winning Powerball – This Thursday’s Powerball Division 1 prize pool is $120 million. It’s huge – the second biggest Division One trophy in history. More than 175 million tickets have been sold for a total of $213 million, equivalent to seven tickets for every living Australian.
But should we play? The answer might surprise you. Powerball naivety has three main levels and then a bonus level.
What Is The Odds Of Winning Powerball
I mainly care about Powerball because my dad plays it from time to time. He is an educated man with a successful career behind him, but he likes the idea of a big prize.
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The first thing to know is the low chance of winning Division One with a single entry. Really really small, as the following diagram shows. Division Nine, on the other hand, is divided.
Powerball is owned by Tabcorp and they put a lot of attention on the Division One prize every week, but it is not awarded every week. Far from it.
All of the last six draws have gone without a Division One winner. Such streaks are not unusual. About three to four drawings end without anyone winning Division 1, so the grand prize is won about once a month:
The following graph shows the gray lines when the Division One prize has not been won and the prize for the following week.
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This is important as awards under Division 1 are not worth writing. Division 9, which you have a 1 in 66 chance of winning, is just over $10. As the following chart shows, even Division 2, where you only have a one in seven million chance of winning, regularly pays in the mid $ 100,000s. Often even less. Most of these other rewards are simply not worth the hype.
Powerball jackpot structure is different every week. Which made me think of. Maybe, just maybe, Powerball can sometimes have a positive expected value. isn’t it? They make a series of drawings where the Division 1 prize does not disappear. They must have been very profitable. Maybe that’s how they make their money? And if the price grows to a high enough, big jackpot, these weeks can have a positive expected value for the player. Maybe if you only played under certain conditions, you
What we need here is a very brief introduction to the concept of expected value, which I call EV. It’s an extremely useful concept, and it’s simple: your expected profit is the chance of winning multiplied by the profit. And the expected value is the expected benefit minus the cost.
For example, if you give me a $2 reward for correctly tossing a coin, my expected reward is $1. If you charge me $1 per trade, my expected value is zero. If you increase the reward to $2.10, my expected value becomes positive.
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Knowledge of electric cars is really powerful: they tell you what to do. If the EV is positive, you should play that game or do as much as possible. If they are negative, you should run away.
You have a negative EV when you play roulette in a casino. In roulette, the combination of winning odds and prizes is designed to give the player a negative EV and the casino a positive EV. It’s a great game for them in the long run and a terrible game for us. If you repeatedly play with negative EVs, you will lose a lot.
The EV concept is also suitable for real situations, not just for games. Well placed depends on the rating of electric cars, for example, and even different postgraduates can have different electric cars. You can extend the expected value to any domain where there is possibility or uncertainty.
For us, the electric car is the most important thing we need to know to decide whether to play Powerball. (Supposing you just don’t like the prospect of holding the flag and letting your mind dream freely).
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How do we find out the expected winnings of the Powerball drawing? Let’s take a look at the smallest drawing of this year, with a $3 million Division One prize. To get a rough estimate, we can simply multiply the probability of winning each division by the price. The following diagram shows the results of the calculation.
As you can see, Division 9 does most of the heavy lifting here. Your one in 66 chance to return about $10.20 will be a little more than 15 cents. A 1 in 134 million chance of winning $3 million is only worth 2.2 cents!
If you subtract the entry fee of $1.21, the electric car is a huge negative. You really shouldn’t play for such a small jackpot.
With a bigger Division 1 prize, could your electric car start? Of course yes. We again use a simplified technique – we multiply the chance of winning by the announced price. Here, the bigger the price, the bigger the expected profit.
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Because in the next drawing, this Thursday, the Division One prize is $120 million. That would seem to change things. One in 134 million chance to win $ 120 million worth 89.5 cents alone in Division 1. The lower divisions are consistently worth over 40 cents of expected profit. Add them to 89.5 cents and the expected profit is $1.30 – higher than the cost of the ticket! EV
A few years ago I asked myself this question about the Powerball drawing with the big Division One prize. My back of the envelope told me the EV was positive and I should play.
I quickly learned that when some people win Division 1, they share the prize. Your chances of winning a ticket are the same, but if you split them, your winnings will be split. As the following chart shows, Division One has been relegated 34 times in recent years and has been split between multiple winners 4 times.
The number of tickets sold increases as the division one jackpot increases. And the higher the number of tickets sold, the greater the chance of multiple allocation winners.
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You can see the effect in the graphic above – three of the seven major Division One trophies have multiple winners.
So the simple calculation I used above – the chance of winning multiplied by the advertised prize – is misleading
Have the same winning numbers, whether it’s for your giant check ceremony, steal the light, split your pot and rain on your parade.
Check out the $150 million prize in 2019. Think you’re playing for $150 million — the good folks at Powerball HQ encourage you to think so — but when lightning strikes and your 1 in 134 million chance of winning numbers come true . , you also discover that your desired price is actually only $50 million dollars. (Sure, $50 million is good, but $150 million isn’t, right?)
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Here’s the part that really excited me: I wanted to measure this. If there is a relationship between the announced Division One prize and the number of tickets sold, and between tickets sold and the probability of multiple winners, can we calculate a more realistic EV for each draw? I wanted to do this since the $150 million jackpot in 2019, but it wasn’t until this year – when I learned to use R – that it became possible.
I scraped data from the internet to calculate the number of entries in each Powerball drawing over the past 20 years. Here’s data from the past four years that shows the stakes increase dramatically as the Division 1 jackpot increases. The red line is a model of a linear relationship.
Is the red line satisfactory? Not really. Can the relationship be non-linear? It can be! The yellow line in the following diagram is a smoothed version of the dots.
Your chance of sharing Division One increases and increases as more people come. And that changes everything.
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This last point is important. Powerball drawings, with Division One prizes less than $110 million, can not possibly have positive electricity. The odds are too bad and the prices too low. But let’s go with high prices from Division 1 – like this week –
And theory has a positive EV. A bend in that yellow line could help the theory become reality.
The math here was a trick when I first realized it – I only solved it after deconstructing the Poisson distribution. The odds of winning Division One are slim. But enough Australians buy Powerball tickets that if the prize gets big, there’s a big chance for multiple winners.
This chart shows just that. Pay attention to the falling white line – this is the probability that no one will win the jackpot, and it drops below 50% when the jackpot is around 80 million. With a Division One prize of just over 100 million, the chances of a winner being one – and only one – are at their peak. After that they fall. Somewhere north of $150 million, the odds of two winners are greater than the odds of one winner.
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This chart also shows that the $150 million Division One prize pool for 2019
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